The shape and size of the superconducting islands and of the
junctions between them
can be well controlled in the fabrication process. It is easy to
notice that while the parameters \(L_n,C_n\)  are mostly determined
by the junction areas, the parasitic ground capacitances
\(C_n^\mathrm {g}\)  are mostly determined by the island sizes. Thus,
the first obvious step is to minimize the island sizes as much as
possible while keeping constant the junction areas, as any part of
the island area which does not participate in the junctions, does
not contribute to the inductance, but decreases \(\omega _1\) . This
optimization was performed in
Refs. [1]}, [2]}, [3]}, [4]}.
Then, the ground capacitance of the \(n\) th island becomes a
function of the areas of the junctions in which it particpates,
\(n-1\)  and \(n\) . This function was calculated numerically in
Ref. [2]}, and the resulting dependence resembles
a weak power law or a logarithm. We will assume that this first
optimization step has been performed.
